Atomic hydrogen or monoatomic hydrogen has been suggested as a rocket
propellant because of its low molecular weight, half that of hydrogen
in its more common H2 form. The problem is storing it because it has
the tendency to recombine to the H2 form:

High temperatures though are known to create atomic hydrogen, and
scramjets by slowing down the hypersonic air stream create high
temperatures in the thousands of degrees Kelvin.
Page 3 of this report gives a graph showing temperatures reached by
the decelerated air stream at hypersonic speeds:

The particular graph is from the work of Nobelist Irving Langmuir. It
shows 9% dissociation at 3000 K, 98% dissociation at 6000 K and 99.99%
at 8000 K. A key fact though is the percent dissociation is dependent
on the total pressure of the hydrogen: at lower pressure the
dissociation is easier and the percentage of atomic hydrogen is higher.
Then to get high percentage of atomic hydrogen at the lower Mach
numbers and lower temperatures we could use hydrogen at lower total
pressure.
To heat the hydrogen however you don't want to mix it with the air as
when you are cumbusting the fuel. This would create a mixture of high
molecular weight, which reduces exhaust velocity. What would be
necessary would be to use efficient heat exchangers to quickly heat the
hydrogen up to the temperature of the decelerated air:

Shooting at the moon.
06 August 1994
NewScientist.com news service
CHARLENE CRABB
"INSTANT HEAT...Hunter does not plan to use electricity to heat the 40
tonnes of hydrogen that will be required for each firing of the JVL.
Instead, the gun will have sophisticated heat exchangers developed at
Brookhaven National Laboratory in New York state that will take just 20
milliseconds to heat this huge quantity of gas to 1200 degree C at a
pressure of only 250 atmospheres. The key to the nearly instantaneous
heating is millimetre-size graphite beads that can absorb the heat
without breaking down. But at these temperatures graphite can react
with hydrogen, so the beads must be covered with thin layers of the
inert compound zirconium oxide. The tiny spheres will be initially
heated by burning methane or propane. The particles will then heat
hydrogen gas as it flows through the bed."
http://www.newscientist.com/article/mg14319373.900.html

Using heat exchangers to heat the hydrogen would also eliminate the
problem of sustaining combustion at the high temperatures produced in
the scramjet engines.

High temperatures though are known to create atomic hydrogen, and
scramjets by slowing down the hypersonic air stream create high
temperatures in the thousands of degrees Kelvin.
Page 3 of this report gives a graph showing temperatures reached by
the decelerated air stream at hypersonic speeds:

Equilibrium chemical composition is a function of the static temperature
and pressure of the constituent, not stagnation temperature. You've made up
a problem which doesn't exist. Time to go back and review basic
thermodynamics and gas dynamics.
--
Ed Ruf (Usenet2@EdwardG.Ruf.com)

High temperatures though are known to create atomic hydrogen, and
scramjets by slowing down the hypersonic air stream create high
temperatures in the thousands of degrees Kelvin.
Page 3 of this report gives a graph showing temperatures reached by
the decelerated air stream at hypersonic speeds:

Equilibrium chemical composition is a function of the static temperature
and pressure of the constituent, not stagnation temperature. You've made up
a problem which doesn't exist. Time to go back and review basic
thermodynamics and gas dynamics.
--
Ed Ruf (Usenet2@EdwardG.Ruf.com)

The purpose of citing the report showing stagnation temperatures was
to give an idea of the high temperatures reached when air is slowed
from hypersonic speed to zero.
The same conclusion can be reached from reentry data:

Atmospheric reentry
"Shock layer gas physics
An approximate rule-of-thumb used by heat shield designers for
estimating peak shock layer temperature is to assume the air
temperature in kelvins to be equal to the entry speed in meters per
second. For example, a spacecraft entering the atmosphere at 7.8 km/s
would experience a peak shock layer temperature of 7800 K. This method
of estimation is a mathematical accident and a consequence of peak heat
flux for terrestrial entry typically occurring around 60 km altitude."
http://en.wikipedia.org/wiki/Reentry

And this page shows an ICBM reentry cone can experience temperatures
of 6000 K at Mach 20 to 25:

The idea to be used here is not to alleviate the high stagnation
temperatures as with scramjets and reentry vehicles but to maintain
them by having a blunt body or sharp pointed body always facing into
the hypersonic air stream so that high temperatures are always
maintained in front of them.
Indeed the terminology "air breather" would be somewhat of a misnomer
here since the air would not be used for combustion as with scramjets
but only to heat the hydrogen to high temperatures and which alone
would be the propellant and exhaust.
A couple of key questions are could the high temperature air heat
enough hydrogen to produce sufficient thrust to counteract the drag
produced by slowing the air down to zero?
Could the heat exchanger be made light enough and operate fast enough
for the amount of hydrogen required to be heated?
Let's do a rough calculation toward the first question. Let's say the
air flow in was at the rate of m given in kg/s and say at a speed of
7000 m/s. Then the force backward would be 7000m.
This page gives the exhaust velocity for a rocket engine according to
temperature:

At very high altitudes the exit pressure in the formula is nearly zero
and the velocity equation simplifies to:

V = sqrt[2kRT/((k-1)M)]

If we assume the hydrogen can be heated to 7000 K, then most or all
will dissociate to atomic hydrogen. The molecular weight will be 1 and
monoatomic gases have a ratio of specific heats k of 1.6. So the
velocity will be v = sqrt[2*1.6*8314.5*7000/.6] = 17,618 m/s. This is
about 2.5 times the velocity of the incoming air. So to have net thrust
the mass flow of the hydrogen would have to be at least 1/2.5 times
that of the air flow.

The purpose of citing the report showing stagnation temperatures was
to give an idea of the high temperatures reached when air is slowed
from hypersonic speed to zero.

So what? It's a non-sequiter as far as air-breathing propulsion goes wrt
combustion for the most part. The air is never slowed down anywhere near
that much. Combustor entrance Mach numbers are more like 1/3 to 1/4 of that
of freestream.

At very high altitudes the exit pressure in the formula is nearly zero
and the velocity equation simplifies to:

V = sqrt[2kRT/((k-1)M)]

If we assume the hydrogen can be heated to 7000 K, then most or all
will dissociate to atomic hydrogen. The molecular weight will be 1 and
monoatomic gases have a ratio of specific heats k of 1.6. So the
velocity will be v = sqrt[2*1.6*8314.5*7000/.6] = 17,618 m/s. This is
about 2.5 times the velocity of the incoming air. So to have net thrust
the mass flow of the hydrogen would have to be at least 1/2.5 times
that of the air flow.

I thought this was an air-breathing thread? Why do you even care about
this. Again an issue of no practical concern. Seems the Hyper-X Mach 10
flight cruised just fine with just 3-4% H2 vs air.
--
Ed Ruf (Usenet2@EdwardG.Ruf.com)

The idea was to bring the hypersonic airstream to a complete stop and
use the high temperatures produced to heat hydrogen fuel onboard via
efficient heat exchangers. There would be no combustion involved.
However, it would seem that the best you could do with this would be to
break even: you're assuming the kinetic energy of the air with respect
to the craft can all be converted to heat, and all this heat can be
transferred to the hydrogen then all this heat can be converted back
into kinetic flow for propulsion. The last step of course is where big
losses would occur.
So additionally to this, why not combust the now still air with
further hydrogen? I thought of using the very hot hydrogen already
heated by the heat exchanger but you want to keep the high exhaust
velocity that this achieves, and mixing this with the air reduces this.
So you would use separate hydrogen for this purpose. Now that the air
is still with respect to the craft there is no prolem of the fuel and
air being at different velocities prior to combustion. And the problem
of combusting the fuel with air at temperatures higher than the
dissociation temperature of the combustion products will be eliminated
since the air will now be cooled by the heat exchangers.
Now that the air is still with respect to the craft we can use a
variety of turbojet or rocket engines. The compression ratio will also
be quite high since the air will be stopped from hypersonic speed.

High temperatures though are known to create atomic hydrogen, and
scramjets by slowing down the hypersonic air stream create high
temperatures in the thousands of degrees Kelvin.
Page 3 of this report gives a graph showing temperatures reached by
the decelerated air stream at hypersonic speeds:

Equilibrium chemical composition is a function of the static temperature
and pressure of the constituent, not stagnation temperature. You've made up
a problem which doesn't exist. Time to go back and review basic
thermodynamics and gas dynamics.
--
Ed Ruf (Usenet2@EdwardG.Ruf.com)

The purpose of citing the report showing stagnation temperatures was
to give an idea of the high temperatures reached when air is slowed
from hypersonic speed to zero.
The same conclusion can be reached from reentry data:

Atmospheric reentry
"Shock layer gas physics
An approximate rule-of-thumb used by heat shield designers for
estimating peak shock layer temperature is to assume the air
temperature in kelvins to be equal to the entry speed in meters per
second. For example, a spacecraft entering the atmosphere at 7.8 km/s
would experience a peak shock layer temperature of 7800 K. This method
of estimation is a mathematical accident and a consequence of peak heat
flux for terrestrial entry typically occurring around 60 km altitude."
http://en.wikipedia.org/wiki/Reentry

And this page shows an ICBM reentry cone can experience temperatures
of 6000 K at Mach 20 to 25:

The idea to be used here is not to alleviate the high stagnation
temperatures as with scramjets and reentry vehicles but to maintain
them by having a blunt body or sharp pointed body always facing into
the hypersonic air stream so that high temperatures are always
maintained in front of them.
Indeed the terminology "air breather" would be somewhat of a misnomer
here since the air would not be used for combustion as with scramjets
but only to heat the hydrogen to high temperatures and which alone
would be the propellant and exhaust.
A couple of key questions are could the high temperature air heat
enough hydrogen to produce sufficient thrust to counteract the drag
produced by slowing the air down to zero?
Could the heat exchanger be made light enough and operate fast enough
for the amount of hydrogen required to be heated?
Let's do a rough calculation toward the first question. Let's say the
air flow in was at the rate of m given in kg/s and say at a speed of
7000 m/s. Then the force backward would be 7000m.
This page gives the exhaust velocity for a rocket engine according to
temperature:

At very high altitudes the exit pressure in the formula is nearly zero
and the velocity equation simplifies to:

V = sqrt[2kRT/((k-1)M)]

If we assume the hydrogen can be heated to 7000 K, then most or all
will dissociate to atomic hydrogen. The molecular weight will be 1 and
monoatomic gases have a ratio of specific heats k of 1.6. So the
velocity will be v = sqrt[2*1.6*8314.5*7000/.6] = 17,618 m/s. This is
about 2.5 times the velocity of the incoming air. So to have net thrust
the mass flow of the hydrogen would have to be at least 1/2.5 times
that of the air flow.

The idea was to bring the hypersonic airstream to a complete stop and
use the high temperatures produced to heat hydrogen fuel onboard via
efficient heat exchangers. There would be no combustion involved.
However, it would seem that the best you could do with this would be to
break even: you're assuming the kinetic energy of the air with respect
to the craft can all be converted to heat, and all this heat can be
transferred to the hydrogen then all this heat can be converted back
into kinetic flow for propulsion. The last step of course is where big
losses would occur.

Actually, if there are no losses, this scheme would result in net
thrust, even if no combustion were to occur. You want to expel
the air and the reaction mass at the same speed. What is happening
is that (in the reference frame of the atmosphere) the kinetic
energy of the expelled propellant is being concentrated into
the vehicle.

I've proposed a similar scheme for interstellar vehicles, where
some sort of electromagnetic coupling to the (extremely thin)
interstellar plasma would be used to accelerate onboard reaction
mass backwards. Done properly, this can accelerate a vehicle
that is initially in motion w.r.t. the interstellar medium, and
can do so without violating any conservation laws.